1. Field of the Invention
The present invention relates to a lumped-element low-pass filter, and more particularly, to a lumped-element low-pass filter realized in a multi-layered substrate.
2. Description of the Prior Art
Low-pass filters are widely used as building blocks in circuit designs. They are usually used to filter out unwanted spurious responses and harmonics of higher frequencies. Performance of a low-pass filter is characterized by insertion loss in the passband and rejection in the stopband. The level of rejection in the stopband is mainly determined by the order of the filter. The higher the order of the filter, the better the rejection in the stopband. However, g filter of higher order requires more elements in filter designs, which leads to a larger circuit size and more insertion loss. Shown in FIG. 1 is a prototype circuit of a conventional third order low-pass filter. P11 and P12 are two ports of the filter. L11 and L12 are two inductors, and C13 is a capacitor. In RF circuit designs for modern wireless handheld devices, due to the tight requirement on circuit size, the third-order filter as shown in FIG. 1 is usually employed for a balance between circuit size and filter performance.
In case that the rejection in the stopband of the third-order filter shown in FIG. 1 is not enough to meet the system requirement, an elliptic-type low-pass filter can be employed. Please refer to FIG. 2. FIG. 2 is a prototype circuit of a conventional third-order elliptic-type low-pass filter. Compared with the low-pass filter in FIG. 1, here two additional capacitors C21 and C22 are added in shunt with inductors L21 and L22, respectively. The resulting parallel LC circuits will create a notch in the insertion loss response within the stopband, and a better stopband rejection can be achieved compared to the filter in FIG. 1. Please refer to FIG. 3. FIG. 3 is a diagram of frequency response of a conventional third-order low-pass filter and a conventional third-order elliptic-type low-pass filter. The transverse axis represents frequency, and the vertical axis represents amplitude in dB. A curve S211 is the transmission coefficient of the conventional third-order low-pass filter shown in FIG. 1, and a curve S212 is the transmission coefficient of the conventional third-order elliptic-type low-pass filter shown in FIG. 2. As shown in FIG. 3, there i s a notch at a frequency f 2 in the stopband of the elliptic-type filter, such that a better stopband rejection is achieved. In addition, it can be seen that the curve S212 is sharper than the curve S211 in the transition band, which is usually considered a good characteristic for a low-pass filter.
Low-pass filters of good rejection in the stopband and sharper frequency response in the transition band are desirable, while the larger number of circuit elements and hence the circuit area of higher order filters is unacceptable in modern RF circuit designs. Therefore, the task of designing a low-pass filter with fewer elements and a good rejection in the stopband has become one of the thresholds in advanced development of RF circuits.